JULİA SETLERİ VE LOJİSTİK HARİTA KULLANILARAK GÖRÜNTÜ ŞİFRELEME

Öz

Açık ağlar ve internet üzerinden veri alışverişi hızla büyüdüğü için, verilerin güvenlik açığı incelenecek büyük bir sorun haline gelmektedir. Bu soruna olası bir çözüm olarak ise metin, görüntü, ses, video gibi verilerin şifrelenmesi yöntemi önerilir. Bu işlem yapılacağı zaman Gelişmiş Şifreleme Standardı (AES) gibi klasik şifreleme algoritmaları her zaman birincil seçimdir, ancak görüntü veya video şifreleme söz konusu olduğunda, literatürdeki birçok araştırmaya bakıldığı zaman hesaplama verimliliği nedeniyle yazarların kaos tabanlı şifreleme tekniklerini önerdiği sıkça görülmektedir. Kaos şifrelemenin ana özelliklerine bakıldığında anahtarların rastgeleliği, başlangıç koşullarına duyarlılığı ve daha büyük anahtarlarla çalışıldığında daha verimli sonuçlar elde edildiği göze çarpar. Bu araştırma makalesinde görüntü işleme konusunda kriptografik yeni bir yaklaşım önerilmiştir. Bu yaklaşımda kaotik haritalardan birisi olan lojistik harita ile julia fraktal setlerinin birlikte kullanılarak bir şifreleme algoritması sunulmaktadır. Yaklaşımda fraktal tabanlı setin kullanılmasının sebebi anahtarın gücünün arttırılarak şifrelemenin daha başarılı olmasını sağlamasıdır. Bu algoritma iki anahtarın işlemden geçirilmesiyle oluşturulan yeni anahtarın görüntü şifrelemede kullanılması ile ortaya çıkmıştır. Buna ilave olarak da algoritmanın başarı oranının arttırılması için çalışmalar yapılmıştır. Sunulan yeni yaklaşımla birlikte oluşan şifreli görüntülerin asıl görüntüler ile birlikte analizinin çıkarılması ve yapılan analiz sonucu elde edilen nicel değerler mevcuttur. Bu değerlerin iyileştirilmesi için de algoritmada çeşitli değişiklikler yapılarak testler yapılmıştır. Bu testler sonucunda şifreli görüntü ile asıl görüntünün karşılaştırılarak yöntemin başarısı ölçülmüştür. Bu başarıyı ölçmek için Piksel Sayısı Değişim Hızı (NPCR), Tepe Sinyal Gürültü Oranı (PSNR), Sinyal Gürültü Oranı (SNR), Korelasyon Katsayısı, Birleşik Ortalama Değişen Yoğunluk (UACI), Yapısal Benzerlik İndeks Ölçüsü (SSIM), Entropi ve Yerel Shannon Entropisi, Ortalama Karesel Hata (MSE), Histogram Analizi metrikleri kullanılmıştır.

Anahtar Kelimeler

• Julia Set
• Kaos Teorisi
• Kaotik Görüntü Şifreleme
• Kaotik Harita
• Kripto Analizi

IMAGE ENCRYPTION USING JULIA SETS AND LOGISTIC MAP

Öz

As data exchange over open networks and the internet is growing rapidly, data vulnerability is becoming a major issue to examine. As a possible solution to this problem, the method of encrypting data such as text, images, audio, and video is recommended. When doing this, classical encryption algorithms such as Advanced Encryption Standard (AES) are always the primary choice, but when it comes to image or video encryption, when looking at many studies in the literature, it is often seen that the authors recommend chaos-based encryption techniques due to computational efficiency. Looking at the main features of chaos encryption, the randomness of the keys, sensitivity to initial conditions and more efficient results are obtained when working with larger keys. A new cryptographic approach to image processing is proposed in this research paper. In this approach, an encryption algorithm is presented by using the logistic map, which is one of the chaotic maps, and the julia fractal sets together. The reason for using the fractal-based set in the approach is to increase the strength of the key and ensure that the encryption is more successful. This algorithm has emerged with the use of the new key, which is created by processing two keys, in image encryption. In addition, studies have been carried out to increase the success rate of the algorithm. With the new approach presented, there are quantitative values obtained as a result of the analysis and analysis of the encrypted images together with the original images. In order to improve these values, various changes were made in the algorithm and tests were carried out. As a result of these tests, the success of the method was measured by comparing the encrypted image with the original image. To measure this success, Pixel Count Rate of Change (NPCR), Peak Signal to Noise Ratio (PSNR), Signal to Noise Ratio (SNR), Correlation Coefficient, Combined Average Variable Intensity (UACI), Structural Similarity Index Measure (SSIM), Entropy, and Local Shannon Entropy, Mean Squared Error (MSE), Histogram Analysis metrics were used.

Anahtar Kelimeler

• Chaos Theory
• Chaotic Image Encryption
• Chaotic Map
• Crypto Analysis
• Julia Set

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